Default reasoning with qualified syllogisms

Abstract

Prior works by the author have introduced the system QUAL (herein Q) of qualified syllogisms. An example of such a syllogism is "Most birds can fly; Tweety is a bird; therefore, it is likely that Tweety can fly." Q provides a formal language for expressing such syllogisms, together with a semantics which validates them. Also introduced in the prior works is the notion of a path logic. Reformulating Q as a path logic allows for the expression of modifier combination rules, such as "From likely P and unlikely P, infer uncertain P." The present work builds on this, showing how to incorporate Q into a system for default reasoning. Here is introduced the notion of a dynamic reasoning system (DRS), consisting of a path logic, together with a semantic net, or more exactly, a taxonomic hierarchy that allows for multiple inheritance. The taxonomic hierarchy enables definition of a specificity relation, which can then be used in default reasoning (more specific information takes priority over less specific). Modifier combination rules prescribe what to do when defaults are applied in the context of multiple inheritance. Propositions derived in this manner all bear qualitative likelihood modifiers, representing the extent to which the proposition is believed.